Duncan, who spent his entire 19-year playing career with the Spurs, replaced Gregg Popovich, who missed the road contest against the Hornets because of personal business, the team announced before the game.
Earlier this season, Duncan was named the acting head coach when Popovich was ejected during a loss to the Portland Trail Blazers on Nov. 16.
Duncan has been an assistant coach on Popovich's coaching staff since July 2019. The former NBA All-Star collaborated with assistants Will Hardy and Becky Hammon during the Spurs' 104-103 comeback victory over the Hornets on Tuesday.
Popovich is expected to return for the Spurs' next game against the Brooklyn Nets on Friday night.
Duncan, 43, won five NBA titles with San Antonio and will be inducted into the Naismith Memorial Basketball Hall of Fame later this year.
The Spurs entered Tuesday's matchup against the Hornets with a 25-34 record, four games behind the Memphis Grizzlies for the No. 8 seed in the Western Conference.